Asymptotic behavior of Toeplitz determinants with a delta function singularity

  title={Asymptotic behavior of Toeplitz determinants with a delta function singularity},
  author={Vanja Mari'c and Fabio Franchini},
  journal={Journal of Physics A: Mathematical and Theoretical},
We find the asymptotic behaviors of Toeplitz determinants with symbols which are a sum of two contributions: one analytical and non-zero function in an annulus around the unit circle, and the other proportional to a Dirac delta function. The formulas are found by using the Wiener–Hopf procedure. The determinants of this type are found in computing the spin-correlation functions in low-lying excited states of some integrable models, where the delta function represents a peak at the momentum of… 

Resilience of the topological phases to frustration

The effects of the introduction of frustrated boundary conditions on several models supporting (symmetry protected) topological orders, and compare their results with the ones obtained with different boundary conditions show that topological phases of one-dimensional systems are in general not affected by topological frustration.

Quantum phase transition induced by topological frustration

In quantum many-body systems with local interactions, the effects of boundary conditions are considered to be negligible, at least for sufficiently large systems. Here we show an example of the

Topological Frustration can modify the nature of a Quantum Phase Transition

Ginzburg-Landau theory of continuous phase transitions implicitly assumes that microscopic changes are negligible in determining the thermodynamic properties of the system. In this work we provide

The frustration of being Odd: the e(cid:27)ects of defects

It has been recently proven that new types of bulk, local order can ensue due to frustrated boundary condition, that is, periodic boundary conditions with an odd number of lattice sites and

The Frustration of being Odd: Resilience of the Topological Phases

Recently it was highlighted that one-dimensional antiferromagnetic spin models with frustrated boundary conditions, i.e. periodic boundary conditions in a ring with an odd number of elements, may

Fate of local order in topologically frustrated spin chains

It has been recently shown that the presence of topological frustration, induced by periodic boundary conditions in an antiferromagnetic XY chain made of an odd number of spins, prevents the

Effects of defects in the XY chain with frustrated boundary conditions

It has been recently proven that new types of bulk local order can ensue due to frustrated boundary condition, that is, periodic boundary conditions with an odd number of lattice sites and



Aspects of Toeplitz Determinants

We review the asymptotic behavior of a class of Toeplitz (as well as related Hankel and Toeplitz + Hankel) determinants which arise in integrable models and other contexts. We discuss Szego,

Theory of Toeplitz Determinants and the Spin Correlations of the Two-Dimensional Ising Model. III

We consider the rectangular Ising model on a half-plane of infinite extent and study some of the consequences connected with the presence of the boundary. Only the spins on the boundary row are

Quantum Ising chains with boundary fields

We present a detailed study of the finite one-dimensional quantum Ising chain in a transverse field in the presence of boundary magnetic fields coupled with the order-parameter spin operator. We

Szegö via Jacobi

An Introduction to Integrable Techniques for One-Dimensional Quantum Systems

This monograph introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to

Rigorous proof for the nonlocal correlation function in the transverse Ising model with ring frustration.

It is proved that all the low excited energy states forming the gapless kink phase share the same asymptotic correlation function with the ground state, and the thermal correlation function almost remains constant at low temperatures if one assumes a canonical ensemble.

Quantum transitions driven by one-bond defects in quantum Ising rings.

It is shown that the quantum scaling phenomena driven by lower-dimensional defects in quantum Ising-like models shows a universal scaling behavior, which is characterized by computing, either analytically or numerically, scaling functions for the low-level energy differences and the two-point correlation function.

Two Soluble Models of an Antiferromagnetic Chain

The Two-Dimensional Ising Model

Toeplitz Determinants: Some Applications, Theorems, and Conjectures